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r-irber-irbe/proof-skills/skills/isabelle-isar-adapter/SKILL.md

isabelle-isar-adapter

Skill3 starsChanged 25 days agoApache-2.0View on GitHub

USE FOR: translating Isabelle/HOL and Isar proofs (locales, transfer, HOL-Analysis) into Lean 4. DO NOT USE FOR: Rocq ports (@rocq-proof-adapter) or HOL/Metamath (@hol-metamath-adapter). TRIGGERS: Isabelle, Isar, locale, lift_definition, transfer, Sledgehammer, Isabelle to Lean.

The file

We split this skill into the rules it gives an agent

3 rules. About 0 are common, 0 are distinctive, and 3 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 3

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    Load Dialect & Concordance Map: Read references/dialects/isabelle.json and query lean_search(source: "concordance") for CONC-01..20.

    line 40
  2. Very specific:

    STOP: when porting (f ⤏ l) (at x within s): Isabelle's at x within s excludes x (𝓝[s \ {x}] x), whereas Mathlib's 𝓝[s] x includes x!

    line 52
  3. Very specific:

    STOP: if an Isabelle type definition relies on non-emptiness (typedef) where the Lean Type* requires an [Inhabited α] or [Nonempty α] …

    line 56

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Isabelle/HOL & Isar Structured Proof Adapter (isabelle_hol -> lean4)

Translate Isabelle/HOL theories (.thy) -- including structured Isar blocks (fix / assume / obtain / have / moreover / ultimately / show), locale hierarchies, Krauss function packages, Lifting & Transfer, and HOL-Analysis filter/measure proofs -- into idiomatic Lean 4.

Routing

  • USE FOR: porting Isabelle/HOL .thy files, Archive of Formal Proofs (AFP) developments, seL4/word theories, and HOL-Analysis / HOL-Probability proofs into Lean 4 + Mathlib4.
  • DO NOT USE FOR: Rocq/Coq .v ports (delegate to @rocq-proof-adapter); HOL Light .ml or Metamath .mm ports (delegate to @hol-metamath-adapter).
  • TRIGGERS: Isabelle, Isar, .thy, locale, interpretation, obtain ... where, also have, finally show, lift_definition, by transfer, sledgehammer, meson.

Workflow

  1. Load Dialect & Concordance Map: Read references/dialects/isabelle.json and query lean_search(source: "concordance") for CONC-01..20.
  2. Translate Locales & Type Definitions (CONC-04, CONC-13, CONC-14):
    • Single-carrier locale / class -> Lean 4 class ([Group G]).
    • Multi-carrier locale -> Lean 4 bundled structure or multi-parameter typeclass ([Module R M]).
    • quotient_type + lift_definition + by transfer -> Quotient + Quotient.lift + Quotient.inductionOn.
  3. Translate Isar Structured Blocks (CONC-02, CONC-06):
    • fix x assume h: "P x" -> intro x h.
    • obtain w where hw: "Q w" using h by blast -> obtain ⟨w, hw⟩ := h.

Recovery & STOP

  • STOP when porting (f ⤏ l) (at x within s): Isabelle's at x within s excludes x (𝓝[s \ {x}] x), whereas Mathlib's 𝓝[s] x includes x! Verify whether x ∈ s matters before choosing 𝓝[≠] x vs 𝓝 x.
  • STOP if an Isabelle type definition relies on non-emptiness (typedef) where the Lean Type* requires an [Inhabited α] or [Nonempty α] typeclass hypothesis.

Handoffs

  • Predecessors: skill:lean-gateway, skill:itp-cross-porting, skill:lean-specification.
  • Successors: skill:lean-proof, skill:lean-proof-review, skill:lean-axiom-closure.

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/isabelle-isar-adapter-handbook.md .

See also

  • ../../references/isabelle-isar-adapter-handbook.md -- Complete isabelle-isar-adapter Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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